Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 12 Sequences and Series - 12.3 Analyze Geometric Sequences and Series - 12.3 Exercises - Problem Solving - Page 815: 57b



Work Step by Step

From part (a), we know that $a_n= a_1 r^{n-1}$ ...(1) Here, we have Common Ratio $r=2$ and first term $a_1=5$ Equation (1) gives: $a_n=5 \times (2)^{n-1}$ We know that $S_{n}=a_1(\dfrac{r^{n}-1}{r-1})$ Now, $S_{4}=5[\dfrac{1-(2)^{4}}{1-2}]$ $S_{4}=5[\dfrac{1-16}{-1}]$ This gives: $S_{4}=5 \times \dfrac{-15}{-1}$ Hence, $S_{4}=75$
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